Lab #7: The Carnot Cycle

 

Reading Assignment:

 

Halliday, Resnick, and Walker, Chapter 21, Sections 1-5

 

Introduction:

 

In the early nineteenth century, a French scientist, Sadi Carnot (1796-1832) studied the thermodynamic processes in which mechanical energy was obtained from thermal energy. The ideal gas cyclic engine has taken his name and is now called the Carnot cycle. This cycle involves four reversible processes, ie. 4 steps that are carried out infinitely slowly and which can be considered a series of thermodynamic equilibrium states each of which can be reversed with no change in the magnitudes of the work done or heat absorbed.

 

A typical Carnot cycle is shown in the figure below:

 

                               

 

The cycle consists of the following four steps:

 

  1. Starting at point 1, the system undergoes an isothermal, reversible expansion to point 2 during which an amount of heat (Qin) is absorbed from a hot reservoir at temperature Th.
  2. This step is followed by an adiabatic (ie. Q = 0), reversible expansion to point 3 at a lower temperature, Tc.
  3.  Next the system undergoes an isothermal compression to point 4 during which an amount of heat (Qout) is expelled to a cold reservoir at temperature Tc.
  4. Finally, there is an adiabatic compression (ie. Q = 0) back to the original starting point 1.

 

For each of the steps, the work done may be calculated depending upon the particular process involved. For any isothermal process the work done is given by:

 

            (isothermal process)                  Eq. (1)

 

where n is the number of moles of gas present and R, known as the Gas Constant, has a value of 8.31 J/mol-K.

 

Similarly, the work done during an adiabatic process is given by:

 

           (adiabatic process)           Eq. (2)

 

The resulting efficiency of going around one complete cycle is defined as:

 

    (efficiency)             Eq. (3)

 

As always, at each point the ideal gas equation holds and the 1st Law of Thermodynamics is valid for each process, ie:

 

                                 (Ideal gas law)                          Eq. (4)

 

and

 

                   (1st Law of Thermodynamics)              Eq. (5)

 

 

Goals for this activity:

 

·        To study the various steps in a Carnot cycle

·        To calculate the values for Q, W and DEint for each step in the cycle

·        To determine the ideal efficiency for a particular Carnot cycle

 

 

Lab #7: The Carnot Cycle

 

Name:_______________________________                                    Section #:________

Name:_______________________________

Name:_______________________________

 

Discussion Questions:

 

 

Consider a cyclic heat engine that undergoes the following cycle using 2 moles of an ideal monatomic gas:

 

Step A: an isothermal expansion at 727oC from 1 m3 to 4 m3;

Step B: an adiabatic expansion to 327oC;

Step C: an isothermal compression at 327oC; and

Step D: an adiabatic compression back to the initial conditions.

 

  1. Draw the four steps on a p-V diagram. Be sure to label the axes, the directions of each of the steps and the temperatures of any isotherms.

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. How much work (in Joules) is done by the engine in step A?

 

 

 

 

 

 

 

 

  1. How much heat (in calories) is absorbed by the gas in step A?

 

 

 

 

  1. What value of g should you use for this gas?

 

 

 

 

 

  1. What is the volume after step B?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. How much work (in Joules) is done in step B?

 

 

 

 

 

 

 

 

 

  1. What is the Carnot efficiency of this engine?

 

 

 

 

 

 

 

  1. How much heat (in calories) is expelled to the cold reservoir in each cycle?

 

 

 

 

 

 

  1. What is the net work (in Joules) done by the gas in each cycle?

 

 

 

 

 

 

 

 

 

  1. Using your results from above (or otherwise) complete the table below:

 

 

W (in J)

DQ (in J)

DEint (in J)

Step A

 

 

 

 

Step B

 

 

 

 

Step C

 

 

 

 

Step D

 

 

 

 

For the cycle